If z_1,z_2,z_3 are complex numbers such that |z_1|=|z_2|=|z_3|= | 1z_1+ 1z_2+ 1z_3 |=1 then |z_1+z_2+z_3| is

Question

Accepted Answer

Correct answer: 1. (1) 1=( 1z_1+ 1z_2+ 1z_3)=( z_1z_1z_1+ z_2z_2z_2+ z_3z_3z_3) ( ∵ |z_1 |^2=1=z_1z_1 ,etc ) = |z_1+z_2+z_3 |= |z_1+z_2+z_3 |= |z_1+z_2+z_3 | ( ∵ (z_1 ) ∃z_1 ∣ )

$If z_{1}, z_{2}, z_{3} are complex numbers such that ∣ z_{1} ∣ = ∣ z_{2} ∣ = ∣ z_{3} ∣ = \frac{1}{z _{1}} + \frac{1}{z _{2}} + \frac{1}{z _{3}} = 1 then ∣ z_{1} + z_{2} + z_{3} ∣ is$

Solution

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